Economic Time Series Models Research Articles

Time Series Simulation by Conditional Generative Adversarial Net

Generative Adversarial Net (GAN) has proved to be a powerful machine learning tool in image data analysis and generation. In this paper, we propose to use Conditional Generative Adversarial Net (CGAN) to learn and simulate time series data. The conditions include both categorical and continuous variables with different auxiliary information. Our simulation studies show that CGAN has the capability to learn different types of normal and heavy-tailed distributions, as well as dependent structures of different time series. It also has the capability to generate conditional predictive distributions consistent with training data distributions. We also provide an in-depth discussion on the rationale behind GAN and the neural networks as hierarchical splines to establish a clear connection with existing statistical methods of distribution generation. In practice, CGAN has a wide range of applications in market risk and counterparty risk analysis: it can be applied to learn historical data and generate scenarios for the calculation of Value-at-Risk (VaR) and Expected Shortfall (ES), and it can also predict the movement of the market risk factors. We present a real data analysis including a backtesting to demonstrate that CGAN can outperform Historical Simulation (HS), a popular method in market risk analysis to calculate VaR. CGAN can also be applied in economic time series modeling and forecasting. In this regard, we have included an example of hypothetical shock analysis for economic models and the generation of potential CCAR scenarios by CGAN at the end of the paper

Time Series Simulation by Conditional Generative Adversarial Net

Generative Adversarial Net (GAN) has been proven to be a powerful machine learning tool in image data analysis and generation. In this paper, we propose to use Conditional Generative Adversarial Net (CGAN) to learn and simulate time series data. The conditions can be both categorical and continuous variables containing different kinds of auxiliary information. Our simulation studies show that CGAN is able to learn different kinds of normal and heavy tail distributions, as well as dependent structures of different time series and it can further generate conditional predictive distributions consistent with the training data distributions. We also provide an in-depth discussion on the rationale of GAN and the neural network as hierarchical splines to draw a clear connection with the existing statistical method for distribution generation. In practice, CGAN has a wide range of applications in the market risk and counterparty risk analysis: it can be applied to learn the historical data and generate scenarios for the calculation of Value-at-Risk (VaR) and Expected Shortfall (ES) and predict the movement of the market risk factors. We present a real data analysis including a backtesting to demonstrate CGAN is able to outperform the Historic Simulation, a popular method in market risk analysis for the calculation of VaR. CGAN can also be applied in the economic time series modeling and forecasting, and an example of hypothetical shock analysis for economic models and the generation of potential CCAR scenarios by CGAN is given at the end of the paper.

Non-Linearities, Structural Breaks and Fractional Integration in the Analysis of the Ghanaian and the South African CPI Inflation Rates

Keeping a low steady rate of inflation is one of the government’s most important responsibilities. Inflation is an important determinant of economic growth. Consequently, it has been one of the most examined areas in economics, from both theoretical and empirical perspectives. Indeed, economists have shown continued interest in this essential economic variable. The most important question related to inflation is: Does non-linearity exist in inflation? The answer to this question, which has important policy implications, can support or endanger the validity of several important economic models. Hence, a clear understanding of the changing aspects of inflation is crucial to any economy because it is regarded as a significant variable in a number of economic models, whose legitimacy critically relies on whether or not this variable is stationary. In practice, many economic time series models rely on linearity. Nonetheless, it has often been found that simple linear time series models regularly leave certain aspects of economic and financial data inexplicable. This paper proposes a model that combines fractional integration with non-linear deterministic terms based on the Chebyshev polynomials in time for the analysis of CPI inflation rates of Ghana and South Africa in Sub-Saharan Africa. Firstly, we tested for non-linear deterministic terms in the context of fractional integration. The estimates of the differencing parameter, d, were found to be 1.11 and 1.32, respectively for the Ghanaian and the South African inflation rates, but the non-linear trends were found to be statistically insignificant in the two series. A linear model was then investigated and the results indicated that the order of integration for the Ghanaian inflation series was slightly above 1. However, for the case of South Africa, a cyclical I(d) process was found to be more appropriate, with an order of integration below 1, thus showing mean reversion and a cyclical structure of approximately 80 periods (months) per cycle. The implication of these findings could assist in a decision-making process regarding adjusting monetary policy instruments such as inflation targeting (IT) or adopting different monetary policies, to achieve the desired target.

Catching the curl: Wavelet thresholding improves forward curve modelling

Modelling futures term structures (price forward curves) is essential for commodity-related investments, portfolios, risk management, and capital budgeting decisions. This paper uses a novel strategy, wavelet thresholding, to de-noise futures price data prior to estimation in a state-space framework in order to improve model fit and prediction. Rather than de-noise the raw data, this method de-noises only wavelet coefficients linked to specific timescales, minimizing the amount of information that is accidentally removed. Our findings are that, for the first five futures maturities in our sample data, in-sample (tracking) and 5-day-ahead out-of-sample (forecasting) Root Mean Squared Errors (RMSEs) are smaller both (i) when we increase the number of factors from one to four, and (ii) when we de-noise the data using wavelet thresholding. The improvement due to wavelet thresholding is often greater than the improvement from adding one more factor to the model, which is important because going beyond four factors does not improve model fit. Wavelet-based de-noising thus has the potential to improve considerably the estimation of various economic time series models, helping practitioners and policymakers with better forecasting and risk management.

Time Series Models with a Common Stochastic Variance for Analysing Economic Time Series

The linear Gaussian state space model for which the common variance is treated as a stochastic time-varying variable is considered for the modelling of economic time series. The focus of this paper is on the simultaneous estimation of parameters related to the stochastic processes of the mean part and the variance part of the model. The estimation method is based on maximum likelihood and it requires the subsequent uses of the Kalman filter to treat the mean part and sampling techniques to treat the variance part. This approach leads to the evaluation of the exact likelihood function of the model subject to simulation error. The standard asymptotic properties of maximum likelihood estimators apply as a result. A Monte Carlo study is carried out to investigate the small-sample properties of the estimation procedure. We present two illustrations which are concerned with the modelling and forecasting of two U.S. macroeconomic time series: Inflation and industrial production.

Unit Root Tests: The Role of the Univariate Models Implied by Multivariate Time Series

In cointegration analysis, it is customary to test the hypothesis of unit roots separately for each single time series. In this note, we point out that this procedure may imply large size distortion of the unit root tests if the DGP is a VAR. It is well-known that univariate models implied by a VAR data generating process necessarily have a finite order MA component. This feature may explain why an MA component has often been found in univariate ARIMA models for economic time series. Thereby, it has important implications for unit root tests in univariate settings given the well-known size distortion of popular unit root test in the presence of a large negative coefficient in the MA component. In a small simulation experiment, considering several popular unit root tests and the ADF sieve bootstrap unit tests, we find that, besides the well known size distortion effect, there can be substantial differences in size distortion according to which univariate time series is tested for the presence of a unit root.

Modelling of Economic Time Series and the Method of Cointegration

The article is focused on the problem of modelling multidimensional non-stationary cointegrated processes. It is a modern method especially used for the description of multidimensional economic time series. The multidimensional process Yt is called cointegrated with the cointegrating vector β, if the process β´Yt is stationary or trend-stationary. For instance this property can be found in some series of economic indices which are predominantly non-stationary. Methods connected with estimates of cointegrating vectors and with a cointegration testing are applied to economic data. All the methods given were programmed in the computing environment MATLAB.

A review of copula models for economic time series

This survey reviews the large and growing literature on copula-based models for economic and financial time series. Copula-based multivariate models allow the researcher to specify the models for the marginal distributions separately from the dependence structure that links these distributions to form a joint distribution. This allows for a much greater degree of flexibility in specifying and estimating the model, freeing the researcher from considering only existing multivariate distributions. The author surveys estimation and inference methods and goodness-of-fit tests for such models, as well as empirical applications of these copulas for economic and financial time series.

Bayesian Inference on Dynamic Models with Latent Factors

In time series analysis, latent factors are often introduced to model the heterogeneous time evolution of the observed processes. The presence of unobserved components makes the maximum likelihood estimation method more difficult to apply. A Bayesian approach can sometimes be preferable since it permits to treat general state space models and makes easier the simulation based approach to parameters estimation and latent factors filtering. The paper examines economic time series models in a Bayesian perspective focusing, through some examples, on the extraction of the business cycle components. We briefly review some general univariate Bayesian dynamic models and discuss the simulation based techniques, such as Gibbs sampling, adaptive importance sampling and finally suggest the use of the particle filter, for parameter estimation and latent factor extraction.

On the Practice of Bayesian Inference in Basic Economic Time Series Models using Gibbs Sampling

textabstractSeveral lessons learned from a Bayesian analysis of basic economic time series models by means of the Gibbs sampling algorithm are presented. Models include the Cochrane-Orcutt model for serial correlation, the Koyck distributed lag model, the Unit Root model, the Instrumental Variables model and as Hierarchical Linear Mixed Models, the State-Space model and the Panel Data model. We discuss issues involved when drawing Bayesian inference on regression parameters and variance components, in particular when some parameter have substantial posterior probability near the boundary of the parameter region, and show that one should carefully scan the shape of the posterior density function. Analytical, graphical and empirical results are used along the way.

J. DENIS SARGAN AND THE ORIGINS OF LSE ECONOMETRIC METHODOLOGY

I review the part played by John Denis Sargan in the formation of the “LSE approach” to dynamic econometric modeling. Despite his unassuming demeanor and his location at LSE—which had earlier dismissed a substantive role for econometric evidence—Sargan nevertheless radically altered the econometric approach of a generation, establishing a powerful approach to empirical modeling of economic time series. His main contributions to econometric methodology, and the subsequent research, are discussed as a complement to the other papers in this memorial volume.Financial support from the U.K. Economic and Social Research Council under grant L138251009 is gratefully acknowledged. I am indebted to Alok Bhargava, Julia Campos, Meghnad Desai, Neil Ericsson, Toni Espasa, Grayham Mizon, Peter Phillips, Timo Terasvirta, and Ken Wallis for helpful comments and to Peter Phillips for the invitation to contribute this paper to Econometric Theory.

RECENT ADVANCES IN MODELLING SEASONALITY

Abstract. In this paper we review recent developments in econometric modelling of economic time series with seasonality. The prime focus is on econometric models which incorporate explicit descriptions of seasonal variation, instead of removing this variation using a seasonal adjustment method. This review centres around developments in seasonal unit root models and in periodic parameter models, both in the univariate and multivariate context. Several empirical examples are used for illustration. We also discuss several areas for further research.

Current Issues in Industrial Economics

Introduction and overview - recent developments in industrial economics, J. Cable economics of the firm, G. Stewart alternative forms of productive enterprise, S. Estrin conjectural variations, C. Fraser oligopoly and welfare, J. Cable et al models of product differentiation, M. Waterson entry and market share mobility, P. Geroski strategic research and development and innovation, J. Beath et al recent developments in the economics of public utility regulation, T. Weyman-Jones linear and non-linear models of economic time series - an introduction, D. Byers and D. Peel.

Cointegration tests on MARS

Multivariate adaptive regression spline (MARS) models due to Friedman (1991) are employed to examine non-linear cointegration. Critical values of the Dickey-Fuller cointegration test statistics, appropriate to the MARS model, are presented. Several empirical examples demonstrate the gains to the non-linear modelling of economic time series.

Recent developments of economic time series models

Recent developments of economic time series models

Dynamic structural analysis and forecasting of residential electricity consumption

This paper studies the dynamic relationships between electricity consumption and several potentially relevant variables, such as weather, price, and consumer income. Monthly data from January 1969 to December 1990 for all-electric residences in the southeast United States are used for this study. Because of the nature of the annual weather cycle, several of these time series are highly seasonal. Multiple-input transfer function models are employed to analyze the data for their dynamic structure and to evaluate future levels of electricity consumption. The linear transfer function (LTF) method is employed in the identification of transfer function models for structural analysis and forecasting. A major finding is that price plays a major role in explaining conservation behavior by electricity consumers. This result has important implications for forecasting the consumption of electric energy. This paper also demonstrates the appropriate construction of models for economic time series with strong seasonality.

Nonlinear dynamics and econometrics: AN introduction

The empirical modelling of economic time series is dominated by methods that assume linearity of the underlying dynamic economic system, the so-called Frisch-Slutsky paradigm. The main a priori argument in favour of linearity and the reason for its original adoption is its simplicity: autoregressive models can be estimated using standard regression packages and there is now a wide range of computer software packages available to estimate models with linear moving average components; the dynamics contained in estimated models can be completely characterized by their impulse response functions and directly related to linear models of the macroeconomy. The dominance of the Frisch-Slutsky paradigm is not based on any strong a priori belief that the economic system is linear. Indeed, once curvature is introduced into utility functions and/or production functions, nonlinearity is pervasive in theoretical dynamic models, hence the shortage of 'closed-form' solutions. Nor is it based on any convincing empirical evidence that actual economic time series are best described as linear stochastic processes. The LQ optimization approach (namely Linear constraints and Quadratic objective functions) which underlies most econometric applications (either implicitly or explicitly) is undoubtedly attractive on analytical and computational grounds, but can be highly deficient in areas where economic behaviour is dominated by asymmetric costs of adjustments, irreversibilities, transaction costs or institutional and physical rigidities. The challenge facing applied econometrics in dealing with these issues is truly immense. Reliable statistical techniques are required for detecting dynamic nonlinearities. Stochastic optimization models that are capable of capturing the primary sources of dynamic nonlinearities and are suitable for empirical analysis need to be developed. The possible effects of temporal aggregation, and aggregation across commodities and agents, need to be worked out in the context of nonlinear dynamic models. These are complicated issues, solutions to some of which have eluded us even in the case of linear models, and promise to be far more complicated when we enter the realm of nonlinear dynamic models. It is therefore natural to expect that real progress in the area of nonlinear dynamic econometric models will be slow and hard to come by. Nevertheless, the past two decades have witnessed important advances in the mathematical and statistical analysis of dynamic systems, particularly in physics, epidemiology and meteorology. Many of these developments have already found their way into economics and

The Hamilton model with a general autoregressive component: estimation and comparison with other models of economic time series: Estimation and comparison with other models of economic time series

This paper generalizes the Hamilton model to the important case in which the autoregressive component need not contain a unit root. Using U.S. quarterly real GNP data, the model is estimated and the results are compared to those of Hamilton. Some Monte Carlo evidence for the model is presented, and its in-sample forecasting performance is discussed and compared to the original Hamilton model, the ARIMA model, and the deterministic-time-trend model.

Instrument Variable Methods for Studying Models of Economic Time Series

This paper considers instrumental variables methods for studying linear models-of economic time series. The instrumental variables used in estimating parameters are assumed to be uncorrelated with the disturbance vector but are not restricted to be strictly exogenous. A greatest lower bound on the asymptotic covariance matrices of a family of instrumental variables estimators is derived and characterized. This bound is then compared to bounds derived previously in both the econometrics literature and the engineering literature.

Analysis of Economic Time Series.

Analysis of Economic Time Series: A Synthesis integrates several topics in economic time-series analysis, including the formulation and estimation of distributed-lag models of dynamic economic behavior; the application of spectral analysis in the study of the behavior of economic time series; and unobserved-components models for economic time series and the closely related problem of seasonal adjustment. Comprised of 14 chapters, this volume begins with a historical background on the use of unobserved components in the analysis of economic time series, followed by an Introduction to the theory of stationary time series. Subsequent chapters focus on the spectral representation and its estimation; formulation of distributed-lag models; elements of the theory of prediction and extraction; and formulation of unobserved-components models and canonical forms. Seasonal adjustment techniques and multivariate mixed moving-average autoregressive time-series models are also considered. Finally, a time-series model of the U.S. cattle industry is presented. This monograph will be of value to mathematicians, economists, and those interested in economic theory, econometrics, and mathematical economics.